Greece's search for a government to prevent the country's disorderly exit from the euro ended late last night with still no sign of an agreement.

The chances of any agreement appeared remote after the Radical Left Coalition, Syriza, said it would not attend talks with the country's two other largest parties, due to resume today.

It fell to the Greek President to make a final appeal to politicians to avoid fresh elections. But Karolos Papoulias failed to make a breakthrough during his meeting with the heads of the three parties earlier yesterday. Hopes had hinged on a change of mind from Fotis Kouvelis, who leads a moderate-left group which could help the conservatives and socialists, who came first and third, to get the majority needed to govern.

Should no agreement be found then Greece is expected to vote again – with 17 June being the likely date – under intense pressure over its future in the eurozone. The campaign would be dominated by a clash between parties who believe Greece must meet the terms of its loan agreements with international creditors to stay in the single currency and others who claim that those agreements can be scrapped without falling out of the euro.

"Greeks are caught with a mountain of debt behind them and the cliff's edge of exit from the euro in front of them," said Theodore Pelagidis, a professor of economics at the University of Piraeus.

The European Central Bank (ECB), the German government and Greece's other EU partners have warned Athens that no substantial renegotiation of the most recent €130bn (£104bn) bailout will be allowed.

The country's collapsing economy and continuing pressure for more cuts and reforms from the "troika" – the International Monetary Fund, the EU and the ECB – have exploded Greece's two-party system and led to the rise of Syriza under Alexis Tsipras.

Aware that his party is climbing in the opinion polls, Mr Tsipras has resisted all efforts by other party leaders to draw him into the coalition. Last night, he said: "Syriza refuses to be a left-wing alibi for a government that will continue the policies the people rejected on 6 May."

Mr Tsipras is accused of using the two-day mandate he was given last week to form a government to begin his campaign for fresh elections rather than make any effort at unity.

The conservative New Democracy and socialist Pasok parties could achieve a parliamentary majority of 168 seats if they were able to persuade the Democratic Left to join them.